mirror of
https://github.com/DarkPlacesEngine/gmqcc.git
synced 2025-03-31 15:01:01 +00:00
Fixed pow/exp using fast approximation until the fractional part is hit. Once fractional is reached a binary search is used to get close to the value.
This commit is contained in:
Dale Weiler
parent
759fca6921
commit
d9572e3e30
1 changed files with 415 additions and 118 deletions
533
intrin.c
533
intrin.c
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@ -58,147 +58,427 @@ static GMQCC_INLINE void intrin_reg(intrin_t *intrin, ast_value *const value, as
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vec_push(intrin->parser->globals, (ast_expression*)value);
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}
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#define QC_M_E 2.71828182845905f
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#define QC_M_E 2.718281828459045f
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#define QC_POW_EPSILON 0.00001f
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static ast_expression *intrin_pow (intrin_t *intrin) {
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/*
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* float pow(float x, float y) {
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* float local = 1.0f;
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* while (y > 0) {
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* while (!(y & 1)) {
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* y >>= 2;
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* x *= x;
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*
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* float pow(float base, float exp) {
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* float result;
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* float low;
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* float high;
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* float mid;
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* float square;
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* float accumulate;
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*
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* if (exp == 0.0)
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* return base;
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* if (exp < 0)
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* return 1.0 / pow(base, -exp);
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* if (exp >= 1) {
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* result = pow(base, exp / 2);
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* return result * result;
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* }
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* y--;
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* local *= x;
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* }
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* return local;
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*
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* low = 0.0f;
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* high = 1.0f;
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* square = sqrt(base);
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* accumulate = square;
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* mid = high / 2.0f
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*
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* while (fabs(mid - exp) > QC_POW_EPSILON) {
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* square = sqrt(square);
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* if (mid < exp) {
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* low = mid;
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* accumulate *= square;
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* } else {
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* high = mid;
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* accumulate *= (1.0f / square);
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* }
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* mid = (low + high) / 2;
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* }
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* return accumulate;
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* }
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*/
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ast_value *value = NULL;
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ast_value *arg1 = ast_value_new(intrin_ctx(intrin), "x", TYPE_FLOAT);
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ast_value *arg2 = ast_value_new(intrin_ctx(intrin), "y", TYPE_FLOAT);
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ast_value *local = ast_value_new(intrin_ctx(intrin), "local", TYPE_FLOAT);
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ast_block *body = ast_block_new(intrin_ctx(intrin));
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ast_block *l1b = ast_block_new(intrin_ctx(intrin)); /* loop 1 body */
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ast_block *l2b = ast_block_new(intrin_ctx(intrin)); /* loop 2 body */
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ast_loop *loop1 = NULL;
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ast_loop *loop2 = NULL;
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ast_function *func = intrin_value(intrin, &value, "pow", TYPE_FLOAT);
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ast_function *func = intrin_value(intrin, &value, "pow", TYPE_FLOAT);
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/* arguments */
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vec_push(value->expression.params, arg1);
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vec_push(value->expression.params, arg2);
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/* prepare some calls for later */
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ast_call *callpow1 = ast_call_new(intrin_ctx(intrin), (ast_expression*)value); /* for pow(base, -exp) */
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ast_call *callpow2 = ast_call_new(intrin_ctx(intrin), (ast_expression*)value); /* for pow(vase, exp / 2) */
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ast_call *callsqrt1 = ast_call_new(intrin_ctx(intrin), intrin_func(intrin, "sqrt")); /* for sqrt(base) */
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ast_call *callsqrt2 = ast_call_new(intrin_ctx(intrin), intrin_func(intrin, "sqrt")); /* for sqrt(square) */
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ast_call *callfabs = ast_call_new(intrin_ctx(intrin), intrin_func(intrin, "fabs")); /* for fabs(mid - exp) */
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/* local */
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vec_push(body->locals, local);
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/* prepare some blocks for later */
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ast_block *expgt1 = ast_block_new(intrin_ctx(intrin));
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ast_block *midltexp = ast_block_new(intrin_ctx(intrin));
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ast_block *midltexpelse = ast_block_new(intrin_ctx(intrin));
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ast_block *whileblock = ast_block_new(intrin_ctx(intrin));
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/* assignment to local of value 1.0f */
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/* float pow(float base, float exp) */
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ast_value *base = ast_value_new(intrin_ctx(intrin), "base", TYPE_FLOAT);
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ast_value *exp = ast_value_new(intrin_ctx(intrin), "exp", TYPE_FLOAT);
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/* { */
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ast_block *body = ast_block_new(intrin_ctx(intrin));
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/*
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* float result;
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* float low;
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* float high;
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* float square;
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* float accumulate;
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* float mid;
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*/
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ast_value *result = ast_value_new(intrin_ctx(intrin), "result", TYPE_FLOAT);
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ast_value *low = ast_value_new(intrin_ctx(intrin), "low", TYPE_FLOAT);
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ast_value *high = ast_value_new(intrin_ctx(intrin), "high", TYPE_FLOAT);
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ast_value *square = ast_value_new(intrin_ctx(intrin), "square", TYPE_FLOAT);
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ast_value *accumulate = ast_value_new(intrin_ctx(intrin), "accumulate", TYPE_FLOAT);
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ast_value *mid = ast_value_new(intrin_ctx(intrin), "mid", TYPE_FLOAT);
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vec_push(body->locals, result);
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vec_push(body->locals, low);
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vec_push(body->locals, high);
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vec_push(body->locals, square);
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vec_push(body->locals, accumulate);
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vec_push(body->locals, mid);
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vec_push(value->expression.params, base);
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vec_push(value->expression.params, exp);
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/*
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* if (exp == 0.0)
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* return base;
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*/
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vec_push(body->exprs,
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(ast_expression*)ast_store_new (
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(ast_expression*)ast_ifthen_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)local,
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(ast_expression*)intrin->fold->imm_float[1] /* 1 == 1.0f */
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(ast_expression*)ast_binary_new(
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intrin_ctx(intrin),
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INSTR_EQ_F,
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(ast_expression*)exp,
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(ast_expression*)intrin->fold->imm_float[0]
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),
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(ast_expression*)ast_return_new(
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intrin_ctx(intrin),
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(ast_expression*)base
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),
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NULL
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)
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);
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/* y >>= 2 */
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vec_push(l2b->exprs,
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(ast_expression*)ast_binstore_new (
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/* <callpow1> = pow(base, -exp) */
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vec_push(callpow1->params, (ast_expression*)base);
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vec_push(callpow1->params,
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(ast_expression*)ast_unary_new(
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intrin_ctx(intrin),
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VINSTR_NEG_F,
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(ast_expression*)exp
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)
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);
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/*
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* if (exp < 0)
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* return 1.0 / <callpow1>;
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*/
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vec_push(body->exprs,
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(ast_expression*)ast_ifthen_new(
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intrin_ctx(intrin),
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(ast_expression*)ast_binary_new(
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intrin_ctx(intrin),
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INSTR_LT,
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(ast_expression*)exp,
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(ast_expression*)intrin->fold->imm_float[0]
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),
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(ast_expression*)ast_return_new(
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intrin_ctx(intrin),
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(ast_expression*)ast_binary_new(
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intrin_ctx(intrin),
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INSTR_DIV_F,
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(ast_expression*)intrin->fold->imm_float[1],
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(ast_expression*)callpow1
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)
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),
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NULL
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)
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);
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/* <callpow2> = pow(base, exp / 2) */
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vec_push(callpow2->params, (ast_expression*)base);
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vec_push(callpow2->params,
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(ast_expression*)ast_binary_new(
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intrin_ctx(intrin),
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INSTR_DIV_F,
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(ast_expression*)exp,
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(ast_expression*)fold_constgen_float(intrin->fold, 2.0f)
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)
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);
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/*
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* <expgt1> = {
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* result = <callpow2>;
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* return result * result;
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* }
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*/
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vec_push(expgt1->exprs,
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(ast_expression*)ast_store_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)result,
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(ast_expression*)callpow2
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)
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);
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vec_push(expgt1->exprs,
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(ast_expression*)ast_return_new(
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intrin_ctx(intrin),
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(ast_expression*)ast_binary_new(
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intrin_ctx(intrin),
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INSTR_MUL_F,
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(ast_expression*)result,
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(ast_expression*)result
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)
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)
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);
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/*
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* if (exp >= 1) {
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* <expgt1>
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* }
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*/
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vec_push(body->exprs,
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(ast_expression*)ast_ifthen_new(
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intrin_ctx(intrin),
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(ast_expression*)ast_binary_new(
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intrin_ctx(intrin),
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INSTR_GE,
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(ast_expression*)exp,
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(ast_expression*)intrin->fold->imm_float[1]
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),
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(ast_expression*)expgt1,
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NULL
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)
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);
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/*
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* <callsqrt1> = sqrt(base)
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*/
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vec_push(callsqrt1->params, (ast_expression*)base);
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/*
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* low = 0.0f;
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* high = 1.0f;
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* square = sqrt(base);
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* accumulate = square;
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* mid = high / 2.0f;
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*/
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vec_push(body->exprs,
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(ast_expression*)ast_store_new(intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)low,
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(ast_expression*)intrin->fold->imm_float[0]
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)
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);
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vec_push(body->exprs,
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(ast_expression*)ast_store_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)high,
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(ast_expression*)intrin->fold->imm_float[1]
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)
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);
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vec_push(body->exprs,
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(ast_expression*)ast_store_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)square,
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(ast_expression*)callsqrt1
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)
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);
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vec_push(body->exprs,
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(ast_expression*)ast_store_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)accumulate,
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(ast_expression*)square
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)
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);
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vec_push(body->exprs,
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(ast_expression*)ast_store_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)mid,
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(ast_expression*)ast_binary_new(
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intrin_ctx(intrin),
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INSTR_DIV_F,
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(ast_expression*)high,
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(ast_expression*)fold_constgen_float(intrin->fold, 2.0f)
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)
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)
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);
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/*
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* <midltexp> = {
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* low = mid;
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* accumulate *= square;
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* }
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*/
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vec_push(midltexp->exprs,
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(ast_expression*)ast_store_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)low,
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(ast_expression*)mid
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)
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);
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vec_push(midltexp->exprs,
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(ast_expression*)ast_binstore_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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INSTR_MUL_F,
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(ast_expression*)arg2,
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(ast_expression*)fold_constgen_float(intrin->parser->fold, 0.25f)
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(ast_expression*)accumulate,
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(ast_expression*)square
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)
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);
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/* x *= x */
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vec_push(l2b->exprs,
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(ast_expression*)ast_binstore_new (
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/*
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* <midltexpelse> = {
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* high = mid;
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* accumulate *= (1.0 / square);
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* }
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*/
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vec_push(midltexpelse->exprs,
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(ast_expression*)ast_store_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)high,
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(ast_expression*)mid
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)
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);
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vec_push(midltexpelse->exprs,
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(ast_expression*)ast_binstore_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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INSTR_MUL_F,
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(ast_expression*)arg1,
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(ast_expression*)arg1
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(ast_expression*)accumulate,
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(ast_expression*)ast_binary_new(
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intrin_ctx(intrin),
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INSTR_DIV_F,
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(ast_expression*)intrin->fold->imm_float[1],
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(ast_expression*)square
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)
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)
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);
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/* while (!(y&1)) */
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loop2 = ast_loop_new (
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intrin_ctx(intrin),
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NULL,
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(ast_expression*)ast_binary_new (
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intrin_ctx(intrin),
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INSTR_AND,
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(ast_expression*)arg2,
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(ast_expression*)intrin->fold->imm_float[1] /* 1 == 1.0f */
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),
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true, /* ! not */
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NULL,
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false,
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NULL,
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(ast_expression*)l2b
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);
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/*
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* <callsqrt2> = sqrt(square)
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*/
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vec_push(callsqrt2->params, (ast_expression*)square);
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/* push nested loop into loop expressions */
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vec_push(l1b->exprs, (ast_expression*)loop2);
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/* y-- */
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vec_push(l1b->exprs,
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(ast_expression*)ast_binstore_new (
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/*
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* <whileblock> = {
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* square = <callsqrt2>;
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* if (mid < exp)
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* <midltexp>;
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* else
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* <midltexpelse>;
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*
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* mid = (low + high) / 2;
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* }
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*/
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vec_push(whileblock->exprs,
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(ast_expression*)ast_store_new(
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intrin_ctx(intrin),
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INSTR_STORE_F,
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(ast_expression*)square,
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(ast_expression*)callsqrt2
|
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)
|
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);
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vec_push(whileblock->exprs,
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(ast_expression*)ast_ifthen_new(
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intrin_ctx(intrin),
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(ast_expression*)ast_binary_new(
|
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intrin_ctx(intrin),
|
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INSTR_LT,
|
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(ast_expression*)mid,
|
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(ast_expression*)exp
|
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),
|
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(ast_expression*)midltexp,
|
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(ast_expression*)midltexpelse
|
||||
)
|
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);
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vec_push(whileblock->exprs,
|
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(ast_expression*)ast_store_new(
|
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intrin_ctx(intrin),
|
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INSTR_STORE_F,
|
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(ast_expression*)mid,
|
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(ast_expression*)ast_binary_new(
|
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intrin_ctx(intrin),
|
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INSTR_DIV_F,
|
||||
(ast_expression*)ast_binary_new(
|
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intrin_ctx(intrin),
|
||||
INSTR_ADD_F,
|
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(ast_expression*)low,
|
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(ast_expression*)high
|
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),
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(ast_expression*)fold_constgen_float(intrin->fold, 2.0f)
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)
|
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)
|
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);
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/*
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* <callabs> = fabs(mid - exp)
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*/
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vec_push(callfabs->params,
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(ast_expression*)ast_binary_new(
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intrin_ctx(intrin),
|
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INSTR_SUB_F,
|
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(ast_expression*)arg2,
|
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(ast_expression*)intrin->fold->imm_float[1] /* 1 == 1.0f */
|
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)
|
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);
|
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/* local *= x */
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vec_push(l1b->exprs,
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(ast_expression*)ast_binstore_new (
|
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intrin_ctx(intrin),
|
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INSTR_STORE_F,
|
||||
INSTR_MUL_F,
|
||||
(ast_expression*)local,
|
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(ast_expression*)arg1
|
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(ast_expression*)mid,
|
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(ast_expression*)exp
|
||||
)
|
||||
);
|
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|
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/* while (y > 0) */
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loop1 = ast_loop_new (
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intrin_ctx(intrin),
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NULL,
|
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(ast_expression*)ast_binary_new (
|
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intrin_ctx(intrin),
|
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INSTR_GT,
|
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(ast_expression*)arg2,
|
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(ast_expression*)intrin->fold->imm_float[0] /* 0 == 0.0f */
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),
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false,
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||||
NULL,
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||||
false,
|
||||
NULL,
|
||||
(ast_expression*)l1b
|
||||
);
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/* push the loop1 into the body for the function */
|
||||
vec_push(body->exprs, (ast_expression*)loop1);
|
||||
|
||||
/* return local; */
|
||||
/*
|
||||
* while (<callfabs> > epsilon)
|
||||
* <whileblock>
|
||||
*/
|
||||
vec_push(body->exprs,
|
||||
(ast_expression*)ast_return_new (
|
||||
(ast_expression*)ast_loop_new(
|
||||
intrin_ctx(intrin),
|
||||
(ast_expression*)local
|
||||
/* init */
|
||||
NULL,
|
||||
/* pre condition */
|
||||
(ast_expression*)ast_binary_new(
|
||||
intrin_ctx(intrin),
|
||||
INSTR_GT,
|
||||
(ast_expression*)callfabs,
|
||||
(ast_expression*)fold_constgen_float(intrin->fold, QC_POW_EPSILON)
|
||||
),
|
||||
/* pre not */
|
||||
false,
|
||||
/* post condition */
|
||||
NULL,
|
||||
/* post not */
|
||||
false,
|
||||
/* increment expression */
|
||||
NULL,
|
||||
/* code block */
|
||||
(ast_expression*)whileblock
|
||||
)
|
||||
);
|
||||
|
||||
/* push block and register intrin for codegen */
|
||||
/* return midvalue */
|
||||
vec_push(body->exprs,
|
||||
(ast_expression*)ast_return_new(
|
||||
intrin_ctx(intrin),
|
||||
(ast_expression*)accumulate
|
||||
)
|
||||
);
|
||||
|
||||
/* } */
|
||||
vec_push(func->blocks, body);
|
||||
|
||||
intrin_reg(intrin, value, func);
|
||||
|
||||
return (ast_expression*)value;
|
||||
}
|
||||
|
||||
|
|
@ -302,33 +582,51 @@ static ast_expression *intrin_mod(intrin_t *intrin) {
|
|||
static ast_expression *intrin_exp(intrin_t *intrin) {
|
||||
/*
|
||||
* float exp(float x) {
|
||||
* return pow(QC_M_E, x);
|
||||
* // mul 10 to round increments of 0.1f
|
||||
* return floor((pow(QC_M_E, x) * 10) + 0.5) / 10;
|
||||
* }
|
||||
*/
|
||||
ast_value *value = NULL;
|
||||
ast_call *call = ast_call_new (intrin_ctx(intrin), intrin_func(intrin, "pow"));
|
||||
ast_value *arg1 = ast_value_new(intrin_ctx(intrin), "x", TYPE_FLOAT);
|
||||
ast_block *body = ast_block_new(intrin_ctx(intrin));
|
||||
ast_function *func = intrin_value(intrin, &value, "exp", TYPE_FLOAT);
|
||||
ast_value *value = NULL;
|
||||
ast_call *callpow = ast_call_new (intrin_ctx(intrin), intrin_func(intrin, "pow"));
|
||||
ast_call *callfloor = ast_call_new (intrin_ctx(intrin), intrin_func(intrin, "floor"));
|
||||
ast_value *arg1 = ast_value_new(intrin_ctx(intrin), "x", TYPE_FLOAT);
|
||||
ast_block *body = ast_block_new(intrin_ctx(intrin));
|
||||
ast_function *func = intrin_value(intrin, &value, "exp", TYPE_FLOAT);
|
||||
|
||||
/* push arguments for params to call */
|
||||
vec_push(call->params, (ast_expression*)fold_constgen_float(intrin->fold, QC_M_E));
|
||||
vec_push(call->params, (ast_expression*)arg1);
|
||||
vec_push(value->expression.params, arg1);
|
||||
|
||||
/* return pow(QC_M_E, x) */
|
||||
vec_push(body->exprs,
|
||||
(ast_expression*)ast_return_new(
|
||||
vec_push(callpow->params, (ast_expression*)fold_constgen_float(intrin->fold, QC_M_E));
|
||||
vec_push(callpow->params, (ast_expression*)arg1);
|
||||
vec_push(callfloor->params,
|
||||
(ast_expression*)ast_binary_new(
|
||||
intrin_ctx(intrin),
|
||||
(ast_expression*)call
|
||||
INSTR_ADD_F,
|
||||
(ast_expression*)ast_binary_new(
|
||||
intrin_ctx(intrin),
|
||||
INSTR_MUL_F,
|
||||
(ast_expression*)callpow,
|
||||
(ast_expression*)fold_constgen_float(intrin->fold, 10.0f)
|
||||
),
|
||||
(ast_expression*)fold_constgen_float(intrin->fold, 0.5f)
|
||||
)
|
||||
);
|
||||
|
||||
vec_push(value->expression.params, arg1); /* float x (for param) */
|
||||
/* return <callfloor> / 10.0f */
|
||||
vec_push(body->exprs,
|
||||
(ast_expression*)ast_return_new(
|
||||
intrin_ctx(intrin),
|
||||
(ast_expression*)ast_binary_new(
|
||||
intrin_ctx(intrin),
|
||||
INSTR_DIV_F,
|
||||
(ast_expression*)callfloor,
|
||||
(ast_expression*)fold_constgen_float(intrin->fold, 10.0f)
|
||||
)
|
||||
)
|
||||
);
|
||||
|
||||
vec_push(func->blocks, body); /* {{{ body }}} */
|
||||
vec_push(func->blocks, body); /* {{{ body }}} */
|
||||
|
||||
intrin_reg(intrin, value, func);
|
||||
|
||||
return (ast_expression*)value;
|
||||
}
|
||||
|
||||
|
|
@ -399,10 +697,9 @@ static ast_expression *intrin_fabs(intrin_t *intrin) {
|
|||
(ast_expression*)arg1,
|
||||
(ast_expression*)intrin->fold->imm_float[0]
|
||||
),
|
||||
(ast_expression*)ast_binary_new(
|
||||
(ast_expression*)ast_unary_new(
|
||||
intrin_ctx(intrin),
|
||||
INSTR_SUB_F,
|
||||
(ast_expression*)intrin->fold->imm_float[0],
|
||||
VINSTR_NEG_F,
|
||||
(ast_expression*)arg1
|
||||
),
|
||||
(ast_expression*)arg1
|
||||
|
|
|
|||
Loading…
Reference in a new issue